Hi everyone,

Today i will be sharing with you an interesting exam-based question on using the **Ideal Gas Equation pV = nRT**.

In case that you have forgotten much about **Ideal Gas Law** & the **Ideal Gas Equation**, you can do a quick revision via my previous blog post.

Let’s take a look at the question.

Question:

If the behaviour of gas W is described exactly by the equation pV=nRT, which of the following statement(s) about gas W is correct?

I: The density of gas W at constant pressure is inversely proportional to its temperature

II: One mole of gas W occupies the same volume under the same conditions of temperature and pressure as an ideal gas

III: The volume of a given mass of gas W is doubled if its temperature is raised from 25

^{ o}C to 50^{o}CYou can choose more than one statement to be correct.

Interesting question isn’t it. Perhaps you want to work out your own answer before you scroll down to take a look at my suggested solution.

Suggested Solution:

**Statement I is correct!**

pV = nRT

pV = (mass/Mr)RT

ρ = pMr/RT since ρ = mass / V

At constant pressure with R (gas constant) and Mr (liquid W) being constant, we can prove that ρ is inversely proportional to T.

**Statement II is correct!**

pV = nRT

Under constant temperature and pressure, V will be directly proportional to n.

Therefore, the volume of a gas is directly proportional to the number of moles of the gas present.

**Statement III is incorrect!**

pV = nRT

For a given mass of gas under constant pressure; n, R and P are all constant.

Thus, we will have V directly proportional to T.

Rearranging it, you will see that V/T is a constant.

At 25 ^{o}C: V_{1}/T_{1} = k(constant) and we will have V_{1} = k(273 + 25)

At 50 ^{o}C: V_{2}/T_{2} = k(constant) and we will have V_{2} = k(273 + 50)

Therefore, you can see that V_{2} is not double that of V_{1}.

Statement III is incorrect! Tricky isn’t it? I also almost fall into the trap saying that this statement is correct because the temperature in degree Celsius really doubled and we earlier found out that V is directly proportional to T. Do be aware that it does not mean that when temperature doubled, the volume will be doubled.

**Note: Temperature must always in kelvin (k) in order to use the Ideal Gas Equation pV = nRT**

I am sure you learned something useful today. I will sharing this question with my weekly JC1 and JC2 H2 Chemistry tuition classes too.

Feel free to forward this blog post to your friend, so that we can all learn Chemistry well together. 🙂